This invention relates to couplings and methods for transmitting motion and power from one part to another, and more particularly to collect couplings and methods that clamp or grip a rotatable shaft while transferring power from or to such a shaft. Prior couplings for rotatable shafts have been deficient in that they produced too much heat, used keys or splines that caused backlash, or were difficult to align. Also, prior couplings that required thrust bearings took up so much space that their use was limited. When magnetic triggering was employed, prior devices used an electromagnetic coil that fully encircled part of the apparatus.